IMPLEMENTATION OF PAIRS TRADING STRATEGIES EXECUTED FOR ARBITRAGE GENERATION

Trading Strategy

In finance, a trading strategy is a fixed plan that is designed to achieve a profitable return by going long or short in markets. The main reasons that a properly researched trading strategy helps are its verifiability, quantifiability, consistency, and objectivity

ARBITRAGE

In economics and finance, arbitrage is the practice of taking advantage of a price difference between two or more markets: striking a combination of matching deals that capitalize upon the imbalance, the profit being the difference between the market prices. When used by academics, an arbitrage is a transaction that involves no negative cash flow at any probabilistic or temporal state and a positive cash flow in at least one state; in simple terms, it is the possibility of a risk-free profit after transaction costs. For instance, an arbitrage is present when there is the opportunity to instantaneously buy low and sell high

Pair-Trading

Long one asset against short another (buy the cheap one and sell the expensive one) Mean-Reversion Strategy: Spread between two highly correlated assets tends to mean revert Stock-Picking Strategy: Eliminates systematic market risk and capitalize on mispricing in stocks This report focus on the mean-reversion strategy

Equity

In accounting and finance, equity is the residual value or interest of the most junior class of investors in assets, after all liabilities are paid; if liability exceeds assets, negative equity exists. In an accounting context, shareholders' equity (or stockholders' equity, shareholders' funds, shareholders' capital or similar terms) represents the remaining interest in the assets of a company, spread among individual shareholders of common or preferred stock; a negative shareholders' equity is often referred to as a positive shareholders' deficit.

Index

A statistical measure of change in an economy or a securities market. In the case of financial markets, an index is an imaginary portfolio of securities representing a particular market or a portion of it. Each index has its own calculation methodology and is usually expressed in terms of a change from a base value. Thus, the percentage change is more important than the actual numeric value.

Exchange-Traded Fund - ETF

A security that tracks an index, a commodity or a basket of assets like an index fund, but trades like a stock on an exchange. ETFs experience price changes throughout the day as they are bought and sold.

Trading Instruments

Equity: 50 US stocks from different sectors: Technology, Industrials, Energy, Consumer Staples, Finances, Material, Healthcare

ETF: 13 ETFs replicating index in various countries: Dow Jones, Midcap Value, Midcap Growth, Brazil, Germany, UK, Australia.

Indices: 10 Major Indexes: DJIA, Nasdaq, S&P, DAX, CAC, STI, HSI, Nikkei, etc

Introduction

Search for profitable pairs for the implementation of pair-trading strategies using the method of cointegration Establish a search process and search criteria Explore various pair-trading strategies Analyze results on various trading instruments, i.e. Stocks, ETF, Stock Indices

Stationarity & Cointegration Construct a mean-reverting spread through linear combination Cointegrating factor (the hedge ratio) is determined by the Johansen method Spread is checked to be stationary using the Augmented-Dicky-Fuller test

Pair-Trade Criteria Factors suggesting suitable trading pairs

include: Length: Longest period showing

significant evidence of mean reversion t-statistic: More negative t-statistic

signifying a more statistically significant evidence of mean reversion

TRADING STRATEGIES

Trading pairs are determined from the search procedure using historical data recursively Identified trading pairs are back-tested using historical data to determine the cumulative profit 3 different trading strategies are employed on the 3 different classes of trading instruments

Trading Strategy I

Using calibrated hedge ratio & mean to trade without recalibration or rebalancing Strategy - Buy when z < mean + 0.5 * sigma - Sell when z > mean + 0.5 * sigma Intuition: Assumes mean reversion about the historical long-term mean exist

Trading Strategy II

Adopts a dynamic calibration of hedge ratio & mean for a window of every 10 trading days and used to trade for the next 10 trading days with rebalancing Strategy - Buy when z < mean + 0.5 * sigma - Sell when z > mean + 0.5 * sigma Intuition: Assumes mean reversion about a mean with stochastic drift exist

Trading Strategy III

Using calibrated hedge ratio to trade without recalibration or rebalancing Strategy - Buy when zt < zt-1 + 0.5 * sigma

- Sell when zt > zt-1 + 0.5 * sigma

Intuition: Assumes that mean reversion follows immediately after a price shock

RESULTS & ANALYSIS

Trading Strategy I GR Vs F P&L: -2.44

Trading Strategy I AMZN Vs NYX P&L: 12.63

Trading Strategy II GR Vs F P&L: 20.57

Trading Strategy II MSCI Pac Ex-Jap Vs MSCI UK P&L: 15.82(ETF)

Trading Strategy III AMZN Vs NYX P&L: -40.89

Trading Strategy III DJIA Vs NIKKEI 225 P&L: 6471.68

Trading Strategy I: Analysis Spread is not mean reverting around the historical long-term mean. A trading position is entered into and the position is held for prolonged period as there is no exit signal. Not a feasible trading strategy.

Trading Strategy II: Analysis Shows a higher trading activity compared to Strategy I and is consistently profitable for the pairs analyzed. Apparently the most appropriate pair-trading strategy for Equity.

Trading Strategy III: Analysis Displays inconsistent performance across the pairs analyzed. There is a possibility of huge profits as well as huge losses. This implies that there is no specific reaction to price shocks for equity pair-trading.

Historically…

The pair trading search process is most easily applicable to Equity as there are more individual assets to compare and easier to arrive at profitable pairs. Using the length and t-statistic of mean reversion from the search procedure is a useful indication of profitable pairs for trading. Pair trading performance for ETF and Indices are more consistent as compared to that of Equity.

Conclusion

Trading Strategy I is not an appropriate trading strategy for the classes of trading instruments analyzed as there exists a stochastic drift away from the historical long-term mean. Trading Strategy II is the most appropriate trading strategy for Equity. Trading Strategy II & III are equally appropriate for ETF pair trading. Trading Strategy III is the most profitable trading strategy for Indices however Trading Strategy is appropriate as well.